Iterative Convex Optimization with Control Barrier Functions for Obstacle Avoidance among Polytopes

2026-03-06

AI Summary

This work addresses the geometric complexity of collision avoidance for polyhedral robots navigating environments populated with polyhedral obstacles by proposing an iterative convex optimization framework that integrates exact polyhedral distance computation with control barrier functions. By computing closest points between convex polyhedra to construct supporting hyperplanes, the method generates linear discrete-time control barrier constraints. Coupled with local linearization of system dynamics and robot geometry, this formulation transforms the original non-convex problem into a sequence of convex optimization problems. Notably, this approach is the first to embed exact polyhedral distance within an MPC-DCBF framework, preserving geometric fidelity while guaranteeing convexity at each optimization step. Experiments demonstrate real-time, collision-free navigation in complex mazes, multi-robot settings, and three-dimensional scenarios, achieving millisecond-level computational performance.

Technology Category

• Intelligent Robots: Learning & Optimization for ROB
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Obstacle avoidance of polytopic obstacles by polytopic robots is a challenging problem in optimization-based control and trajectory planning. Many existing methods rely on smooth geometric approximations, such as hyperspheres or ellipsoids, which allow differentiable distance expressions but distort the true geometry and restrict the feasible set. Other approaches integrate exact polytope distances into nonlinear model predictive control (MPC), resulting in nonconvex programs that limit real-time performance. In this paper, we construct linear discrete-time control barrier function (DCBF) constraints by deriving supporting hyperplanes from exact closest-point computations between convex polytopes. We then propose a novel iterative convex MPC-DCBF framework, where local linearization of system dynamics and robot geometry ensures convexity of the finite-horizon optimization at each iteration. The resulting formulation reduces computational complexity and enables fast online implementation for safety-critical control and trajectory planning of general nonlinear dynamics. The framework extends to multi-robot and three-dimensional environments. Numerical experiments demonstrate collision-free navigation in cluttered maze scenarios with millisecond-level solve times.

Problem

• obstacle avoidance
• polytopes
• convex optimization
• model predictive control
• control barrier functions

Innovation

• Control Barrier Functions
• Convex Optimization
• Polytopic Obstacle Avoidance
• Model Predictive Control
• Iterative Linearization